Properties

Label 1620.f
Number of curves $2$
Conductor $1620$
CM no
Rank $1$
Graph

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Show commands: SageMath
E = EllipticCurve("f1")
 
E.isogeny_class()
 

Elliptic curves in class 1620.f

sage: E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
1620.f1 1620d2 \([0, 0, 0, -60912, -5786316]\) \(183711891456/125\) \(17006112000\) \([]\) \(3888\) \(1.2783\)  
1620.f2 1620d1 \([0, 0, 0, -912, -4316]\) \(4045602816/1953125\) \(40500000000\) \([3]\) \(1296\) \(0.72902\) \(\Gamma_0(N)\)-optimal

Rank

sage: E.rank()
 

The elliptic curves in class 1620.f have rank \(1\).

Complex multiplication

The elliptic curves in class 1620.f do not have complex multiplication.

Modular form 1620.2.a.f

sage: E.q_eigenform(10)
 
\(q + q^{5} + 2 q^{7} - 3 q^{11} - 4 q^{13} - 6 q^{17} - 7 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

sage: E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the LMFDB numbering.

\(\left(\begin{array}{rr} 1 & 3 \\ 3 & 1 \end{array}\right)\)

Isogeny graph

sage: E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with LMFDB labels.